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Partial Least Squares (PLS) has been shown to be a versatile regression technique with an increasing number of applications in the areas of process control, process monitoring and process analysis. This Thesis considers the area of nonlinear PLS; a nonlinear projection based regression technique. The nonlinearity is introduced as a univariate nonlinear function between projections, or to be more specific, linear combinations of the predictor and the response variables. As for the linear case, the method should handle multicollinearity, underdetermined and noisy systems. Although linear PLS is accepted as an empirical regression method, none of the published nonlinear PLS algorithms have achieved widespread acceptance. This is confirmed from a literature survey where few real applications of the methodology were found. This Thesis investigates two nonlinear PLS methodologies, in particular focusing on their limitations. Based on these studies, two nonlinear PLS algorithms are proposed. In the first of the two existing approaches investigated, the projections are updated by applying an optimization method to reduce the error of the nonlinear inner mapping. This ensures that the error introduced by the nonlinear inner mapping is minimized. However, the procedure is limited as a consequence of problems with the nonlinear optimisation. A new algorithm, Nested PLS (NPLS), is developed to address these issues. In particular, a separate inner PLS is used to update the projections. The NPLS algorithm is shown to outperform existing algorithms for a wide range of regression problems and has the potential to become a more widely accepted nonlinear PLS algorithm than those currently reported in the literature. In the second of the existing approaches, the projections are identified by examining each variable independently, as opposed to minimizing the error of the nonlinear inner mapping directly. Although the approach does not necessary identify the underlying functional relationship, the problems of overfitting and other problems associated with optimization are reduced. Since the underlying functional relationship may not be established accurately, the reliability of the nonlinear inner mapping will be reduced. To address this problem a new algorithm, the Reciprocal Variance PLS (RVPLS), is proposed. Compared with established methodology, RVPLS focus more on finding the underlying structure, thus reducing the difficulty of finding an appropriate inner mapping. RVPLS is shown to perform well for a number of applications, but does not have the wide-ranging performance of Nested PLS.

Thesis (Ph. D.)--Stanford University, 1987. / "June 1987." This research was supported in part by Joseph Oliger under Office of Naval Research contract N00014-82-K-0335, by Stanford Linear Accelerator Center and the Systems Optimization Laboratory under Army Research Office contract DAAG29-84-K-0156. Includes bibliographies.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 91-94).

Thesis (M.S.)--Brigham Young University. Dept. of Statistics, 2004. / Includes bibliographical references (p. 28-29).

Thesis (M.S.)--University of Wisconsin--Madison, 1969. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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This study was designed to describe the experiences of general education students in elementary settings where the inclusion of students with disabilities was responsibly implemented. The research question investigated was: Do general education students have a meaningful opportunity to learn when sharing classrooms with students with disabilities? The participants in this study were assigned to two inclusion classrooms in an elementary school in northeastern North Carolina. The classrooms were observed during the months of January and February, 1999. Effective educational practices in inclusion classrooms were researched. Data were also collected and analyzed in four areas: (1) principal and teachers' definitions of inclusion, (2) principal and teachers' perceptions of how inclusion is implemented in the school, (3) effects of inclusion on teachers' instructional practices, and (4) effects of inclusion on the learning opportunities for general education students. There were no observable effects of inclusion on the learning opportunities for general education students. / Ed. D.

Thesis (M.S.)--South Dakota State University, 1990. / Includes bibliographical references (leaves 47-51).